A080134 - OEIS

%I #8 Apr 28 2016 21:16:03

%S 5,3,3,2,4,3,2,3,3,1,1,3,1,4,1,1

%N Conjectured number of generalized Fermat primes of the form (n+1)^2^k + n^2^k, with k>=0.

%C Values of k <= 16 were tested. The sequence A078902 lists some of the generalized Fermat primes. Bjorn and Riesel examined generalized Fermat numbers for n <= 11 and k <= 999. The next n>1 for which (n+1)^2^k + n^2^k is prime for k=0,1,2,3,4 is n=826284.

%H Anders Björn and Hans Riesel, <a href="http://www.jstor.org/stable/2584996">Factors of Generalized Fermat Numbers</a>, Mathematics of Computation, Vol. 67, No. 221, Jan., 1998, pp. 441-446.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/GeneralizedFermatNumber.html">Generalized Fermat Number</a>

%e a(1) = 5 because there are five known Fermat primes: 3, 5, 17, 257, 65537.

%t lst={}; Do[prms=0; Do[If[PrimeQ[(n+1)^2^k+n^2^k], prms++ ], {k, 0, 16}]; AppendTo[lst, prms], {n, 16}]; lst

%Y Cf. A019434, A078902, A080131, A080133.

%K nonn,hard,more

%O 1,1

%A _T. D. Noe_, Jan 30 2003